If you want realism, understand that armor was really expensive and rare outside of nobles. What would really happen is you walk up to a blacksmith and commission a set. He'll take your measurements, get the details and half the pay (or however much they agree on) and then work on it for the next five months. You might not want to make them wait that long, though a short delay gives them a very good reason to stick around for longer than they might otherwise.

If he wasn't doing commissions for the nobles, the blacksmith is manufacturing stock items to keep up a healthy inventory, and is usually paid by the military. Most blacksmiths made and repaired tools, not weapons or armor, although their facilities worked for either.

Of course, only high-value items warranted their own shops. Everything else is bought, sold and bartered at the market. A good market has hundreds of vendors, competing with each other and their customers for good prices. I don't have any idea of what haggling system you'd prefer, but I think you get the idea.

Medieval Cities had specialized shops for almost everything. A city with actual walls would have freemen who were chandlers, butchers, leatherworkers, smiths, etc. with their own shops, typically with their family living in the second story of the building.

Market towns (pop a few hundred) are much more likely to have the everything is sold at the market vibe. But usually only twice a week or something. You probably would be entirely unable to find serious armor there.

It's a common misconception that armor was rare or expensive. But any blacksmith would possess the skills and tools to make it. Saxons in Britain routinely wore armor, even those who weren't nobles.

Battlefields without armored soldiers is unheard of.

Of course, they only wore armor to go to war. They never wore it casually, and they never "went adventuring" so you'd never see anyone out and about in armor unless they were marching off to battle.

Edit: To answer the OP's question, if you were in a Medieval Saxon village or fort, you'd go to any one of the smiths and tell them what you wanted, and he'd make it for you. It would likely take a while, but since nobody fought in the winter, that's probably when you'd "go shopping" if you knew that you were likely to need armor come spring.

Edit again: A lot of folks confuse "medieval" with "renaissance" era, which overlap a bit but aren't quite the same. During the renaissance, armor was pretty much for show, and was a very expensive sort of thing that was worn on parade, because by then, folks had started using weapons like longbows, crossbows, and guns even cannons, which rendered armor somewhat moot and therefore impractical. So renaissance armor is likely to be worn by nobles and be pretty expensive.

But if you're looking for medieval realism, your armor is likely to be mail of interlocking rings over cloth and/or leather, with maybe a few hard pieces for the chest, shins, and the like. Many of these pieces don't actually need to be made to fit an individual.

Full plate does, but outside of parades and sporting events like jousting, there wasn't actually a whole lot of usage of plate armor on the battlefield. Most folks in full plate would have been riding into battle as cavalry or dragoons, and those guys were expensive, well-trained, and quite possibly your nobles, or men who were hired by nobles.

Another bit of realism: The quiver doesn't go on the back. It goes at the waist, on the left if you're right-handed. Putting it on the back will put your arrows out of easy reach.

Also, Saxons liked to use gauntlets in battle. Really thick metallic gloves. They would stand close together in a scrimmage, and poke their swords through their mail-gloved fists like you wield a pool cue. Imagine a line of 50 pissed off Saxons with gladius-sized pool cues coming at you. Screaming. Once the scrimmage line broke up, they'd spread out and start swinging their swords, but they'd try to kill the enemy without resorting to that, because it's tiring.

Also, they'd use a mercy blade or finishing knife, or sometimes a skull hammer, to finish off an opponent with the off hand, once the opponent had been stuck with the sword. Two hits, and you're dead.

Both these comments are legitimate but to figure out how I would do it in game is characters also need downtime to learn skills etc (level up) so I would say that if they want new armor they would have to do it at the times their character can level. You can't level in combat or even on the road. you may have the experience but not the rest or mind frame to focus on your experiences and realize the lessons learned. Thus while out on the road armor cannot be purchased but while waiting (as they level) between adventures they can. This gives the players time to work on character sheets etc so your not wasting time. Especially if the casters are learning new spells etc then that is when armor can be commissioned etc. Also, they can commission armor before they leave and come back at another time.